If in doubt, take your friend out

AskOxford: Which is correct: 'my friend and me' or 'my friend and I'?:

"I am the subject of the sentence, but the object of the sentence is me.

If in doubt, take your friend out of the sentence.

Me and my friend went to a party last night. [Wrong]
I and my friend went to a party last night.

My friend and me went to a party last night. [Wrong]
My friend and I went to a party last night.

The mayor has invited me and my husband.
The mayor has invited I and my husband. [Wrong]

The mayor has invited my husband and me.
The mayor has invited my husband and I. [Wrong]

Incidentally, saying 'my friend and I' instead of 'I and my friend' is not better grammar, it's just being polite."